Question

If f(x)=2x^6+x^5+32x+32, is (x+2) a factor of f(x).

Answer 1

Answer: By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0

f(- 2)

= 2(-2)^{6} + -2)^{5} + 32(- 2) + 32

= 2(64) - 32 - 64 + 32

= 128 - 32 - 64 + 32

= 64 ≠ 0

Hence (x + 2) is not a factor of f(x)

Answer 2

No

Explanation:

By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0

f(- 2)

= 2
`(-2)^(6)` +
`-2)^(5)` + 32(- 2) + 32

= 2(64) - 32 - 64 + 32

= 128 - 32 - 64 + 32

= 64 ≠ 0

Hence (x + 2) is not a factor of f(x)